Existence of positive solutions for a boundary value problem of nonlinear fractional differential equations.

In this paper, we investigate the existence and multiplicity results of positive solutions for a boundary value problem of nonlinear fractional differential equations. The differential operator is taken in the Riemann-Liouville sense and the nonlinear term depends on the fractional derivative of an unknown function. We derive first the associated Green's function and prove its properties. Consequently, the considered problem is deduced to an equivalent integral equation. Next, by means of the Leggett-Williams fixed point theory, we obtain the existence and multiplicity results of positive solutions. [ABSTRACT FROM AUTHOR]